Bøger udgivet af Friedrich Vieweg & Sohn Verlagsgesellschaft mbH

This volume contains contributions to the BRI-TE/EURAM, Area 5, pilot phase programme on the validation of computational fluid dynamics (CFD) codes, EUROVAL. Two-and three-dimensional flows are investigated with particular emphasis on precise comparison against measurements.

This volume contains 22 papers presented at the Kiel Seminar in 1992. The Kiel Seminars are well known, and cover special areas in numerical methods for partial differential equations, numerical linear algebra, numerical methods for integral equations and related areas.

11 The GAMM Committee for Efficient Numerical Methods for Partial 11 Differential Equations organises workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various types of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such workshops was continued in 1991, January 25- 27, with the 7th Kiel-Seminar on the special topic 11 11 Numerical techniques for boundary element methods at the Christian-Albrechts-University of Kiel. The seminar was attended by 57 scientists from 8 countries. The list of topics contained applications of the boundary element method (BEM) to various problems of practical interest, algo­ rithmic aspects of the BEM (coupling with finite element method, parallelisation), convergence analysis, and in particular the treatment of the numerical integration. In six contributions the quadrature of weakly singular, Cauchy singular, and hypersingular integrals is analysed. 11 11 The editor thanks the DFG-Schwerpunkt Randelementmethoden for its support. He also likes to express his gratitude to all persons involved in the organisation of the seminar.

The most frequently used method for the numerical integration of parabolic differential equa­ tions is the method of lines, where one first uses a discretization of space derivatives by finite differences or finite elements and then uses some time-stepping method for the the solution of resulting system of ordinary differential equations. Such methods are, at least conceptually, easy to perform. However, they can be expensive if steep gradients occur in the solution, stability must be controlled, and the global error control can be troublesome. This paper considers a simultaneaus discretization of space and time variables for a one-dimensional parabolic equation on a relatively long time interval, called 'time-slab'. The discretization is repeated or adjusted for following 'time-slabs' using continuous finite element approximations. In such a method we utilize the efficiency of finite elements by choosing a finite element mesh in the time-space domain where the finite element mesh has been adjusted to steep gradients of the solution both with respect to the space and the time variables. In this way we solve all the difficulties with the classical approach since stability, discretization error estimates and global error control are automatically satisfied. Such a method has been discussed previously in [3] and [4]. The related boundary value techniques or global time integration for systems of ordinary differential equations have been discussed in several papers, see [12] and the references quoted therein.

This volume is dedicated to Pierre Dolbeault, with contributions to complex analysis and analytic geometry. Contributors include Pierre Lelong, V. Ancona, B. Gaveau, B. Berndtsson, E.M. Chirka, E.L. Stout, J.P. Demailly, K. Diederich, G. Herbort, P. Dolbeault and G. Henkin.

Bringing together experts in the field of harmonic maps and integrable systems to give a coherent account of this subject, this book starts with introductory articles. Harmonic maps are maps between Riemannian or pseudo-Riemannian manifolds which extremize a natural energy integral.

"A publication of the Max-Planck-Institut f'ur Mathematik, Bonn."

Autonomous mobile systems (AMS) are systems capable of some mobility and equipped with advanced sensor devices in order to flexibly respond to changing environmental situations, thus achieving some degree of autonomy.

The book is meant to be primarily a textbook. Therefore most of the examples of special thermodynamic systems are standards in different fields. The number of the examples, however, is restricted. For more applications we refer the reader to the rich literature on thermodynamics. The author hopes that the book, which is concerned above all with basic connections, will be interesting not only for students but also for academic teachers and other scientists who like the structural analysis of fundamentals in physics. According to the character of a textbook, this book is not intended to demonstrate new results. Nevertheless, the way of the logical deductions, and of the presentations used in this book, as well as the choice of illustrating examples are not only influenced by literature but also by discussions with colleagues and friends. In this respect I should like to mention the Professors A. Stahl, J. Meixner, R. Bausch, H.-K. Janssen, R. Bessenrodt, Dr. E. Scholl, and Dr. C. Escher in Germany, as well as Professor C. A. Mead in Minneapolis, and Professor R. St. Berry in Chicago. Particular thank is directed to Professor V. Dohm for critically reading certain parts of the manuscript and making valuable proposals for improvements.

"Vous avez faites erreur, Monsieur, vous auriez du suivre les cours de Weierstraß a. Berlin. C'est notre maitre a. tous." Mit diesen Worten begrüßte HERMITE 187- zwei Jahre nach dem deutsch-französischen Krieg - den jungen MITTAG-LEFFLER in Paris. Besser läßt sich wohl kaum ausdrücken, wie hoch das Ansehen war, wel­ ches WEIERSTRASS damals weltweit genoß. Er war 1856 nach vierzehn Jahren im preußischen Schuldienst nach Berlin berufen worden. Hier entfaltete er alsbald eine umfangreiche Lehrtätigkeit. Sein Programm "Einleitung in die Funktionentheorie, Elliptische Funktionen, Abelsche Funktionen, Variationsrechnung" hat er dreißig Jahre im viersemestrigen Zyklus (durch)gehalten. Welch ein Triumph für jemanden, der jahrelang u.a. Deutsch, Geographie, Schönschreiben und 'lUmen unterrichten mußte. Die 6-stündige "Einleitung in die Theorie der analytischen Funktionen" war die erfolgreichste WEIERSTRAss-Vorlesung. A. KNESER erinnert sich an die 80er Jahre: "Seine Vorlesungen hatten sich damals zu hoher auch äußerer Vollendung entwik­ kelt." Bekannte Mathematiker haben Mitschriften der "Einleitung ... " angefertigt, so W. KILLING (SS 1868) und A. HURWITZ (SS 1878). Der KILLING-Text wurde jüngst veröffentlicht. Das vorliegende Buch gibt die HURWITZ-Mitschrift wieder. HURWITZ, damals 19 Jahre jung, leistet Erstaunliches: schon früh meinte man, die Mitschrift sei womöglich besser als die Vorlesung selbst. KLEIN und WEIERSTRASS selbst grif­ fen auf diese Nachschrift zurück.

This text introduces at a moderate speed and in a thorough way the basic concepts of the theory of stochastic integrals and Ito calculus for sem i­ martingales. There are many reasons to study this subject. We are fascinated by the contrast between general measure theoretic arguments and concrete probabilistic problems, and by the own flavour of a new differential calculus. For the beginner, a lot of work is necessary to go through this text in detail. As areward it should enable her or hirn to study more advanced literature and to become at ease with a couple of seemingly frightening concepts. Already in this introduction, many enjoyable and useful facets of stochastic analysis show up. We start out having a glance at several elementary predecessors of the stochastic integral and sketching some ideas behind the abstract theory of semimartingale integration. Having introduced martingales and local martingales in chapters 2 - 4, the stochastic integral is defined for locally uniform limits of elementary processes in chapter S. This corresponds to the Riemann integral in one-dimensional analysis and it suffices for the study of Brownian motion and diffusion processes in the later chapters 9 and 12.

Presents an approach to the formal object-oriented specification of information systems. The approach focuses on the early phases of system development where existing systems have to be described or systems to be developed have to be prescribed (conceptional modelling).

La Reunion is an oceanic intra-plate volcanic island located at the southern-most part 0 of the Mascarene Basin at 21 0 07' S, 55 32' E (Figure 1). It lies south of the Mascarene Plateau and Mauritius Island but is a distinct topographic feature on the rather flat ocean bottom of the Mascarene Basin, whose age is paleocene in the vicinity of the island (Schlich, 1982), and whose lowest point is more than 4000m deep. La Reunion is ellip­ tical in shape (50 X 70 km) with a NW-SE elongation. It is composed of two volcanoes: Piton des Neiges and Piton de la Fournaise. A third volcanic structure has been recent­ ly discovered on the east submarine flank of the island (Unat et aI. , submitted). Piton des Neiges, a dormant and deeply eroded volcano, rises to a height of 3069 m and oc­ cupies the northwestern two-thirds of the island. Piton de la Fournaise (2630 m), one of the most active basaltic volcanoes in the world, began to grow more than 3. 5 X 1O~ years ago on the southeast flank of Piton des Neiges. The evolution of Piton de la Fournaise (Chevallier and Bachclery, 1981) is marked by the formation of three sub-concentric nested calderas (Figure 2). The boundaries of the two older calderas are more or less buried or eroded.

"A publication of the Max-Planck-Institut f'ur Mathematik, Bonn."

Im Mittelpunkt des Buches steht eine Konstruktion mit Hilfe von Geradenkonfigurationen in der komplex-projektiven Ebene, die überraschende Beziehungen zur elementaren Geometrie aufzeigt: Aus der berühmten Miyaoka-Yau-Ungleichung für die Chernschen Zahlen einer algebraischen Fläche folgen Aussagen über Geraden- und Punktkonfigurationen, für die kein direkter Beweis bekannt ist. Der Grenzfall der Ungleichung ist eine Proportionalitätsbeziehung, die genau die Flächen charakterisiert, deren universelle Überlagerung die Vollkugel im komplex-zweidimensionalen Raum ist. Die Methoden gestatten die Konstruktion von Flächen aus dieser besonders interessanten Klasse, für die bislang wenig explizite Beispiele bekannt waren.

Auf der Erde leben ca. 4,4 Milliarden Menschen. Davon sind 600 Millionen alter als 60 Jahre. Altere Frauen mit einer gro!?,eren Krankheitsanfalligkeit als Manner werden mehr gesundheitlicher und sozialer Betreuung bediirfen. Altere Menschen suchen haufiger den Arzt auf als jiingere. Dieses zeigt sich in einem iiberproportional hohen Anteil an Rent­ nern in den allgemeinen und internistischen Praxen. Altere Menschen haben einen durchschnittlich hohen Arzneimittelverbrauch. Aus Be­ richten verschiedener europaischer Lander geht hervor, da!?' fUr die iiber 60jahrigen 30 bis 40% der Aufwendungen auf Arzneimittel entfallen. 75 % iiber 75 Jahre nehmen sogar regelma!?'ig Arzneimittel ein, 213 davon nehmen 2 bis 3 Medikamente taglich, die Halfte 4 bis 6 Medikamente. Fast 40 % der Frauen iiber 75 Jahre konsumieren regel­ ma!?'ig psychotrope Mittel. Ein Teil der Aufwendungen ist bei iiber 65jahrigen Patienten iiberproportional hoch, namlich bei den Herz-Kreislauferkrankungen, beim Bluthoch­ druck, bei Stoffwechselerkrankungen wie Diabetes und Befindlichkeitsstorungen. Phy­ siologische Alterung und Polymorbiditat fUhren bei alteren Menschen zwangslaufig, zumindest in der Anfangsphase der Behandlung, zu einer Polypragmasie in der Pharma­ kotherapie. Daraus erwachst wiederum die Gefahr, da!?' bei Einnahme mehrerer Medi­ kamente Nebenwirkungen und Interaktionen gehauft auftreten. Auch die Zahl der Todes­ falle durch Nebenwirkungen von Arzneimitteln scheinen mit dem Alter anzuwachsen. Unter 10 000 Obduktionen der Heidelberger und Darmstadter pathologischen Institute wurden morphologische Manifestationen von Arzneimittelschaden in 2,6 % der Falle nachgewiesen. Von 257 Fallen waren 34,6 % mit Arzneimittelschaden die Haupttodes­ ursache.

Contains 14 papers, presented at the Symposium on High Performance Scientific Computing organized by FORTWIHR and held on June 17-18, 1993 in Munich, Germany. The papers give a survey on recent research efforts and industrial applications of numerical simulation in various areas.

This volume contains the 22 contributions of the Workshop on 3D-Computation at Incompressible Internal Flows held in 1989 at the EPFL, Lausanne, Switzerland. This was the first GAMM Workshop on Numerical Methods in Fluid Mechanics developed to a real industrial problem.

Explores the Cretaceous tectonics of the South American Andes region. The book is not only of academic interest, but also because of the economic importance conferred on this portion of the Earth's crust by the hydrocarbon, and other metallic and non-metallic ore resources contained there.

In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro­ duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich­ let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper­ ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza­ tion of Dirichlet's L-functions with a generalization of class field the­ ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.

This monograph contains a selection of papers presented at the Seventh Inter­ national Seminar on Model Optimization in Exploration Geophysics held at the Free University of Berlin, February 8-11, 1989. The papers presented here cover the different methods of synthetic and real data sets. The volume covers a wide spectrum of the subject from basic mathematics, general theory and computer implementation of methods to their practical applications. The first section of the book deals with the basic mathematics and general theory underlying geophysical data inversion. Papers presented here include those dealing with the solution of ill-posed inverse problems, constraint strategies in optimization, spherical spline approximation and the use of integral transforms in geophysical data inversion. The second section contains papers on the inversion of gravity and magnetic data. These papers cover such topics as the use of singular v;alue decomposition and space domain iterative inversion techniques in the study of gravity and magnetic anomalies. Also included here are papers dealing with the stochastic and statistical modelling of potential fields, mass density distribution inside the earth and the mapping of archeological sites through the inversion of magnetic field data.

Usually 15/20 selected contributions, grouped in technical sessions (system modelling and identification, control systems design, computer hardware and soft ware, knowledge-based systems, robotics etc.), are presented at the Workshop, whereby the invited guests preferably present survey papers on current problems of modern systems engineering.

The advent of the high-speed computer with its enormous storage capabilities enabled statisticians as well as researchers from the different topics of life sciences to apply mul tivariate statistical procedures to large data sets to explore their structures.

Originally presented as the author's thesis (doctoral--Technical University, Munich, 1990).

In this paper, a comparison is made of several proof calculi in terms of the lengths of shortest proofs for some given formula of first order predicate logic with function symbols. In particular, we address the question whether, given two calculi, any derivation in one of them can be simulated in the other in polynomial time. The analogous question for propositional logic has been intensively studied by various authors because of its implications for complexity theory. And it seems there has not been as much endeavour in this field in first order logic as there has been in propositional logic. On the other hand, fOr most of the practical applications of logic, a powerful tool such as the language of first order logic is needed. The main interest of this investigation lies in the calculi most frequently used in automated theorem proving, the resolution calculus, and analytic calculi such as the tableau calculus and the connection method. In automated theorem proving there are two important aspects of complexity. In order to have a good theorem proving system, we must first have some calculus in which we can express our derivations in concise form. And second, there must be an efficient search strategy. This book deals mainly with the first aspect which is a necessary condition for the second since the length of a shortest proof always also gives a lower bound to the complexity of any strategy.

This work illustrates two basic principles in the calculus of variations - the questions of existence of solutions and, closely related, the problem of regularity of minimizers. It concentrates on techniques, and presents methods useful for applications in regularity theorems.

Within the DFG -Schwerpunktprogramm "Stromungssimulation mit Hochleistungsrechnern" and within the activities of the French-German cooperation of CNRS and DFG a DFG symposium on "Computational Fluid Dynamics (CFD) on Parallel Systems" was organized at the Institut fur Aerodynamik and Gasdynamik of the Stuttgart University, 9-10 December 1993.

Contains a collection of papers presented at a conference on nonlinear hyperbolic problems held in Taormina, Italy from 3-8 April, 1992. The papers deal with different mathematical techniques of relevant interest to current research in nonlinear wave propagation.

Governments 'Grand Challenge' for 'Aerospace Vehicle Design' for the 1990's: 'Massively parallel computing systems and advanced parallel software technology and algorithms will enable the development and validation of multidisciplinary, coupled methods.

Today's fluid dynamic re search cannot be discussed without supercomputers and since CFD is one of the im portant users of supercomputers, future development of supercomputers has to take the requirements of CFD into account.